Analysis of an SEIRS epidemic model with two delays

Journal of Mathematical Biology
K L Cooke, P van den Driessche

Abstract

A disease transmission model of SEIRS type with exponential demographic structure is formulated. All newborns are assumed susceptible, there is a natural death rate constant, and an excess death rate constant for infective individuals. Latent and immune periods are assumed to be constants, and the force of infection is assumed to be of the standard form, namely proportional to I(t)/N(t) where N(t) is the total (variable) population size and I(t) is the size of the infective population. The model consists of a set of integro-differential equations. Stability of the disease free proportion equilibrium, and existence, uniqueness, and stability of an endemic proportion equilibrium, are investigated. The stability results are stated in terms of a key threshold parameter. More detailed analyses are given for two cases, the SEIS model (with no immune period), and the SIRS model (with no latent period). Several threshold parameters quantify the two ways that the disease can be controlled, by forcing the number or the proportion of infectives to zero.

Citations

Mar 7, 2009·Journal of Mathematical Biology·Michael L Taylor, Thomas W Carr
Sep 28, 2010·Journal of Mathematical Biology·Gang Huang, Yasuhiro Takeuchi
Aug 12, 2006·Bulletin of Mathematical Biology·Shujing GaoZhidong Teng
Nov 10, 2009·Bulletin of Mathematical Biology·Konstantin B Blyuss, Yuliya N Kyrychko
Jan 22, 2010·Bulletin of Mathematical Biology·Gang HuangDaijun Wei
Oct 26, 2012·Bulletin of Mathematical Biology·Subhra Bhattacharya, Frederick R Adler
Aug 6, 2003·Mathematical Biosciences·Juan Zhang, Zhien Ma
Sep 3, 1999·Mathematical Biosciences·M Y LiJ Karsai
Jan 1, 2008·Journal of Biological Dynamics·Tailei Zhang, Zhidong Teng
Aug 18, 2012·Journal of Biological Dynamics·D BredaR Vermiglio
Aug 21, 2012·Mathematical Biosciences and Engineering : MBE·Zhisheng Shuai, P van den Driessche
Aug 31, 2013·Journal of Mathematical Biology·Yuan Yuan, Jacques Bélair
Feb 19, 2016·Journal of Biological Dynamics·Areej AlshormanLibin Rong
Sep 11, 2010·Mathematical Biosciences·Guihong FanHuaiping Zhu
Sep 4, 2015·Theory in Biosciences = Theorie in Den Biowissenschaften·Sanhong LiuXinan Zhang
Jun 3, 2004·Mathematical Biosciences·Wendi Wang, Xiao-Qiang Zhao
Dec 24, 2017·Journal of Mathematical Biology·Isam Al-Darabsah, Yuan Yuan
Feb 23, 2019·Bulletin of Mathematical Biology·Pengfei Song, Yanni Xiao
Apr 21, 2018·Bulletin of Mathematical Biology·Chiu-Ju LinGail S K Wolkowicz
Sep 11, 2017·Journal of Mathematical Biology·Dejun FanDongyan Sun
Aug 25, 2020·Nonlinear Dynamics·Xianbo LiuBalakumar Balachandran
Jan 5, 2019·Journal of Mathematical Biology·Fuxiang Li, Xiao-Qiang Zhao
Nov 6, 2018·Chaos·Subhas KhajanchiDibakar Ghosh
Jan 15, 2021·International Journal of Infectious Diseases : IJID : Official Publication of the International Society for Infectious Diseases·B ShayakAnand Kumar Mishra
Feb 23, 2021·Journal of Applied Mathematics & Computing·Dongchen ShangguanRonghua Tan
Oct 28, 2021·Neurocomputing·César Quilodrán-CasasChristopher C Pain

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